I thought it is interesting to see what the great Nobel Laureate physicist Richard Feynman said about Erwin Schrödinger's attempts to discover the famous Schrödinger equation in quantum mechanics:
When Schrödinger first wrote it [his equation] down,
He gave a kind of derivation based on
some heuristic
Arguments and some brilliant intuitive
guesses. Some
Of the arguments he used were even
false, but that does
Not matter; the only important thing
is that the ultimate
Equation gives a correct description
of nature.
--
Richard P. Feynman
(The Feynman Lectures on Physics, Vol. III, Chapter 16, 1965.)It has been my experience in reading physics books that this sort of `heuristic' reasoning is part of doing physics. It is a very creative (sometimes not logical!) art with mathematics in attempting to understand the physical world. Dirac did it too when he obtained his Dirac equation for the electron.
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